Addition chains for elliptic-curve scalar inversion, found by Tao Tai's Sigrun agent swarm (2026-10-30). Check any file with Python 3, standard
library only:   python3 check.py FILE TARGET     (TARGET = curve25519, p521, p384, p256, secp256k1)

STILL AHEAD OF EVERY PUBLISHED FIGURE WE KNOW (as of 2026-10-30)

curve25519-scalar-279.txt  Curve25519, exponent l - 2: length 279 (247 doublings + 32 other additions).
                           Best published: 283 (mmcloughlin/addchain; additionchains.com lists 283).
                           Public since 2026-09-29: github.com/TTaoGaming/addition-chain-search, commit 75a00af.
p521-scalar-577.txt        NIST P-521, exponent q - 2: length 577 (520 doublings + 57 other additions).
                           No published length found. Found 2026-10-29 (580 -> 579 -> 578 -> 577 that day).

HISTORY: OURS WHEN PUBLISHED, SINCE BEATEN

history/p384-scalar-421.txt      NIST P-384: 421 (380 + 41). Found 2026-09-24, public 2026-09-29 (commit 75a00af).
                                 Published then: 433 (B. Smith 2017). Since beaten: 420, B. Smith (October 2026).
history/p256-scalar-284.txt      NIST P-256: 284 (251 + 33). Public 2026-09-30 (commit c18e65b).
                                 Published then: 292 (B. Smith 2017). Since beaten: 281, B. Smith (October 2026).
history/secp256k1-scalar-288.txt secp256k1: 288 (253 + 35). Public 2026-09-29 (commit aced5d6).
                                 Published then: 290 (B. Smith 2017). Since beaten: 282, B. Smith (October 2026).

Smith's October 2026 lengths are as listed on additionchains.com/LargeChains.html. Format: one integer per line, from 1
to n, as on additionchains.com. All of these are verified upper bounds, not optimal chains.
